In neglect of vertex corrections the thermal conductivity in a nontrivial superconducting state is [1]}, [2]}
\(\kappa =\frac{N_0v^2_F}{12T^2}\int _0^\infty \frac{dE~E^2}{\cosh ^2(E/2T)}\frac{1}{{\text{R}e}~t(E){\text{I}m}~t(E)}{\text{R}e}\frac{|t(E)|^2+t^2(E)-2\Delta ^2}{\sqrt{t^2(E)-\Delta ^2}}.\) 
